Serway & Jewett — Temperature: Problem 29

The pressure gauge on a cylinder of gas registers the gauge pressure, which is the difference between the interior pressure and the exterior pressure \(P_0\). Let’s call the gauge pressure \(P_g\). When the cylinder is full, the mass of the gas in it is \(m_i\) at a gauge pressure of \(P_{gi}\). Assuming the temperature of the cylinder remains constant, show that the mass of the gas remaining in the cylinder when the pressure reading is \(P_{gf}\) is given by \[m_f = m_i \left( \frac{P_{gf} + P_0}{P_{gi} + P_0} \right)\]